Quantitative Problem Solving

Taken from the Complete Assessment Guide for Educators by the GED Testing Service, November 2012 Update

Quantitative Problem Solving
Assessment Targets Content Indicators / CCSS / DOK
Q.1 Apply number sense concepts, including ordering rational numbers, absolute value, multiples, factors, and exponents
Q.1.aOrder fractions and decimals, including on a number line / 4.NF.2
6.NS.6
6.NS.7 / 1-2
Q.1.bApply number properties involving multiples and factors, such as using the LCM, GCF, or distributive property to rewrite numeric expressions / 6.NS.4 / 1-2
Q.1.cApply rules of exponents in numerical expressions with rational exponents to write equivalent expressions with rational exponents / 8.EE.1
N-RN.2 / 1-2
Q.1.dIdentify absolute value or rational number as its distance from 0 on the number line and determine the distance between two rational numbers on the number line, including using the absolute value of their difference / 6.NS.7
7.NS.1 / 1-2
Q.2 Add, subtract multiply, divide and use exponents and roots of rational, fraction and decimal numbers
Q.2.aPerform MDAS on rational numbers / 7.NS.1
7.NS.2 / 1-2
Q.2.bPerform computations and write numerical expressions with squares and square roots of positive, rational numbers / 8.EE.2
N-RN.2 / 1-2
Q.2.cPerform computations and write numerical expressions with cubes and cube roots of positive, rational numbers / 8.EE.2
N-RN.2 / 1-2
Q.2.dDetermine when a numerical expression is undefined / 7.NS.2 / 2
Q.2.eSolve one-step or multi-step arithmetic, real world problems involving the four operations with rational numbers, including those involving scientific notation / 7.NS.3
7.EE.3
8.EE.4
N-Q.1 / 1-2
Q.3 Calculate and use ratios, percents and scale factors
Q.3.aCompute unit rates. Examples include but are not limited to: unit pricing, constant speed, persons per square mile, BTUs per cubic foot. / 6.RP.3
7.RP.1
G-MG.2 / 1-2
Q.3.bUse scale factors to determine the magnitude of a size change. Convert between actual and drawings and scale drawings / 7.G.1 / 1-2
Q.3.cSolve multistep, arithmetic, real-world problems using ratios or proportions including those that require converting units of measure / 6.RP.3
7.RP.1
7.RP.2
7.RP.3
N-Q.1 / 2
Q.3.dSolve two-step, arithmetic, real world problems involving percents. Examples include but are not limited to: simple interest, tax, markups and markdowns, gratuities and commissions, percent increase and decrease. / 7.RP.3 / 1-2
Q.4 Calculate dimensions, perimeter, circumference, and area of two-dimensional figures
Q.4.aCompute the area and perimeter of triangles and rectangles when given area or perimeter / 7.G.6 / 1-2
Q.4.bCompute the area and circumference of circles. Determine the radius or diameter when given area or circumference / 7.G.4 / 1-2
Q.4.cCompute the perimeter of a polygon. Given a geometric formula, compute the area of a polygon. Determine side lengths of the figure when given the perimeter or area / 6.EE.2
7.G.6 / 1-2
Q.4.dCompute perimeter and area of 2-D composite geometric figures, which could include circles, given geometric formulas as needed / 6.EE.2
7.G.6
8.G.9 / 1-2
Q.4.eUse the Pythagorean theorem to determine unknown side lengths in a right triangle / 8.G.7 / 1-2
Q.5 Calculate dimensions, surface area, and volume of three-dimensional figures
Q.5.aWhen given geometric formulas, compute volume and surface area of rectangular prisms. Solve for side lengths or height, when given volume or surface area / 6.EE.2
7.G.6
8.G.9 / 1-2
Q.5.bWhen given geometric formulas, compute volume and surface area of cylinders. Solve for height, radius, or diameter when given volume or surface area. / 6.EE.2
7.G.6
8.G.9 / 1-2
Q.5.cWhen given geometric formulas, compute volume and surface area of right prisms. Solve for side lengths or height, when given volume or surface area. / 6.EE.2
7.G.6
8.G.9 / 1-2
Q.5.dWhen given geometric formulas, compute volume and surface area of right pyramids or cones. Solve for side lengths, height, radius, or diameter when given volume or surface area. / 6.EE.2
7.G.6
8.G.9 / 1-2
Q.5.eWhen given geometric formulas, compute volume and surface area of spheres. Solve for radius or diameter when given the surface area. / 6.EE.2
8.G.9 / 1-2
Q.5.fCompute surface area and volume of composite 3-D geometric figures, given geometric formulas as needed. / 6.EE.2
8.G.9 / 1-2
Q.6 Interpret and create data displays
Q.6.aRepresent, display, and interpret categorical data in bar graphs or circle graphs / 7.RP.2
3.MD.3 / 1-2
Q.6.bRepresent, display, and interpret data involving one variable plots on the real number line including dot plots, histograms, and box plots. / S-ID.1 / 1-2
Q.6.cRepresent, display, and interpret data involving two variables in tables and the coordinate plane including scatter plots and graphs. / 8.SP.1
Q.7 Calculate and use mean, median, mode and weighted average
Q.7.aCalculate the mean, median, mode and range. Calculate a missing data value, given the average and all the missing data values but one, as well as calculating the average, given the frequency counts of all the data values, and calculating a weighted average. / 6.SP.3
S-MD.2
Q.8 Utilize counting techniques and determine probabilities
Q.8.a Use counting techniques to solve problems and determine combinations and permutations / S-CP.9 / 1-2
Q.8.b Determine the probability of simple and compound events / 7.SP.7
7.SP.8
S-CP.1
S-CP.2 / 1-2
Algebraic Problem Solving
Assessment Targets Content Indicators / CCSS / DOK
A.1 Write, evaluate, and compute with expressions and polynomials
A.1.aAdd, subtract, factor, multiply and expand linear expressions with rational coefficients / 7.EE.1 / 1-2
A.1.bEvaluate linear expressions by substituting integers for unknown quantities / 6.EE.2 / 1-2
A.1.cWrite linear expressions as part of word-to-symbol translations or to represent common settings. / 6.EE.2
6.EE.6 / 1-2
A.1.dAdd, subtract, multiply polynomials, including multiplying two binomials, or divide factorable polynomials. / A-APR.1 / 1-2
A.1.eEvaluate polynomial expressions by substituting integers for unknown quantities. / 6.EE.2 / 1-2
A.1.fFactor polynomial expressions / A-SSE.2
A-SSE.3
A-SSE.4 / 1-2
A.1.gWrite polynomial expressions as part of word-to-symbol translations or to represent common settings. / 6.EE.2
6.EE.6 / 1-2
A.1.hMDAS rational expressions / 6.EE.3 / 1-2
A.1.iEvaluate rational expressions by substituting integers for unknown quantities. / 6.EE.2 / 1-2
A.1.jWrite rational expressions as part of word-to-symbol translations or to represent common settings. / 6.EE.2
6.EE.6 / 1-2
A.2 Write, manipulate, and solve linear equations
A.2.aSolve one-variable linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms or equations with coefficients represented by letters / 7.EE.4
8.EE.7
A-REI.3 / 1-2
A.2.bSolve real-world problems involving linear equations / 7.EE.4
A-CED.1
A-CED.2 / 1-2
A.2.cWrite one-variable and multi-variable linear equations to represent context. / 6.EE.6
A-CED.1
A-CED.2 / 1-2
A.2.dSolve a system of two simultaneous linear equations by graphing, substitution, or linear combination. Solve real-world problems leading to a system of linear equations. / 8.EE.6
A-REI.6 / 1-2
A.3 Write, manipulate, solve, and graph linear inequalities
A.3.aSolve linear inequalities in one variable with rational number coefficients. / A-REI.3 / 1-2
A.3.bIdentify or graph the solution to a one variable linear inequality on a number line. / 6.EE.8
7.EE.4 / 1-2
A.3.cSolve real-world problems involving inequalities. / 7.EE.4
A-CED.1
A-CED.2 / 1-2
A.3.dWrite linear inequalities in one variable to represent context / 6.EE.2
A-CED.1
A-CED.2 / 1-2
A.4 Write, manipulate, and solve quadratic equations
A.4.aSolve quadratic equations in one variable with rational coefficients and real solutions, using appropriate methods. (e.g. quadratic formula, completing the square, factoring, inspection) / A-REI.4 / 1-2
A.4.bWrite one-variable quadratic equations to represent context. / A-CED.1 / 1-2
A.5 Connect and interpret graphs and functions
A.5.aLocate points in the coordinate plane / 6.NS.6 / 1
A.5.bDetermine slope of a line from a graph, equation, or table / 8.F.4 / 1-2
A.5.cInterpret unit rate as the slope in a proportional relationship / 8.EE.5 / 2
A.5.dGraph two-variable linear equations / A-CED.2
F-IF.7 / 1-2
A.5.eFor a function that models a linear or nonlinear relationship between two quantities, interpret key features of graphs and tables in terms of quantities, and sketch graphs showing key features of graphs and tables in terms of quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior, and periodicity. / 8.F.3
8.F.5
F-IF.5 / 1-2
A.6 Connect coordinates, lines, and equations
A.6.aWrite the equation of a line with a given slope through a given point. / A-CED.2 / 1-2
A.6.bWrite the equation of a line passing through two given distinct points. / A-CED.2 / 2
A.6.cUse slope to identify parallel and perpendicular lines and the solve geometric problems / G-GPE.5 / 1-2
A.7 Compare, represent, and evaluate functions
A.7.aCompare two different proportional relationships represented in different ways. Examples include but are not limited to: compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. / 8.EE.5 / 2
A.7.bRepresent or identify a function in a table or graph as having exactly one output (one element in the range) for each input (each element in the domain). / 8.F.1
F-IF.1 / 1-2
A.7.cEvaluate linear and quadratic functions for values in their domain when represented using function notation. / F-IF.2 / 1-2
A.7.dCompare properties of two linear or quadratic functions each represented in a different way (algebraically, numerically in tables, graphically or by verbal descriptions). Examples include but are not limited to: given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. / 8.F.2
F-IF.9 / 2